Volatility forecasting for stock market incorporating macroeconomic variables based on GARCH-MIDAS and deep learning models

Empirical experiments have shown that macroeconomic variables can affect the volatility of stock market. However, the frequencies of macroeconomic variables are low and different from the stock market volatility, and few literature considers the low-frequency macroeconomic variables as input indicators for deep learning models. In this paper, we forecast the stock market volatility incorporating low-frequency macroeconomic variables based on a hybrid model integrating the deep learning method with generalized autoregressive conditional heteroskedasticity and mixed data sampling (GARCH-MIDAS) model to process the mixing frequency data. This paper firstly takes macroeconomic variables as exogenous variables then uses the GARCH-MIDAS model to deal with the problem of different frequencies between the macroeconomic variables and stock market volatility and to forecast the short-term volatility and finally takes the predicted short-term volatility as the input indicator into machine learning and deep learning models to forecast the realized volatility of stock market. It is found that adding macroeconomic variables can significantly improve the forecasting ability in the comparison of the forecasting effects of the same model before and after adding the macroeconomic variables. Additionally, in the comparison of the forecasting effects among different models, it is also found that the forecasting effect of the deep learning model is the best, the machine learning model is worse, and the traditional econometric model is the worst.     

Mixed-frequency forecasting of crude oil volatility based on the information content of global economic conditions

This paper subjects six alternative indicators of global economic activity to empirically examine their relative predictive powers in the forecast of crude oil market volatility. GARCH-MIDAS approach is constructed to accommodate all the relevant series at their available data frequencies, thereby circumventing information loss and any associated bias. We find evidence in support of global economic activity as a good predictor of energy market volatility. Our forecast evaluation of the various indicators places a higher weight on the newly developed indicator of global economic activity which is based on a set of 16 variables covering multiple dimensions of the global economy, whereas other indicators do not seem to capture. Furthermore, we find that accounting for any inherent asymmetry in the global economic activity proxies improves the forecast accuracy of the GARCH-MIDAS-X model for oil volatility. The results leading to these conclusions are robust to multiple forecast horizons and consistent across alternative energy sources.     

Forecasting stock market volatility using (non-linear) Garch models

In this paper we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng, 1993) and the Glosten, Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations such as the 1987 stock market crash and that the GJR model cannot be recommended for forecasting.     

Modeling and forecasting realized volatility in German–Austrian continuous intraday electricity prices

This paper uses high‐frequency continuous intraday electricity price data from the EPEX market to estimate and forecast realized volatility. Three different jump tests are used to break down the variation into jump and continuous components using quadratic variation theory. Several heterogeneous autoregressive models are then estimated for the logarithmic and standard deviation transformations. Generalized autoregressive conditional heteroskedasticity (GARCH) structures are included in the error terms of the models when evidence of conditional heteroskedasticity is found. Model selection is based on various out‐of‐sample criteria. Results show that decomposition of realized volatility is important for forecasting and that the decision whether to include GARCH‐type innovations might depend on the transformation selected. Finally, results are sensitive to the jump test used in the case of the standard deviation transformation.     

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

Multifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.     

The Information Content of Intraday Implied Volatility for Volatility Forecasting

This study examines the intraday S&P 500 implied volatility index (VIX) to determine when the index contains the most information for volatility forecasting. The findings indicate that, in general, VIX levels around noon are most informative for predicting realized volatility. We posit that the VIX performs better during this time period because trading motivation around noon is less complex, and therefore trades contain more information on the market expectation of future volatility. Further investigation on the 2008 financial crisis period suggests that market participants become more cautious, and thus the forecasting performance is sustained until the market's close. Copyright © 2015 John Wiley & Sons, Ltd.     

Stock market volatility and the forecasting performance of stock index futures

This study attempts to apply the general equilibrium model of stock index futures with both stochastic market volatility and stochastic interest rates to the TAIFEX and the SGX Taiwan stock index futures data, and compares the predictive power of the cost of carry and the general equilibrium models. This study also represents the first attempt to investigate which of the five volatility estimators can enhance the forecasting performance of the general equilibrium model. Additionally, the impact of the up‐tick rule and other various explanatory factors on mispricing is also tested using a regression framework. Overall, the general equilibrium model outperforms the cost of carry model in forecasting prices of the TAIFEX and the SGX futures. This finding indicates that in the higher volatility of the Taiwan stock market incorporating stochastic market volatility into the pricing model helps in predicting the prices of these two futures. Furthermore, the comparison results of different volatility estimators support the conclusion that the power EWMA and the GARCH(1,1) estimators can enhance the forecasting performance of the general equilibrium model compared to the other estimators. Additionally, the relaxation of the up‐tick rule helps reduce the degree of mispricing. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluating volatility and interval forecasts

A widely used approach to evaluating volatility forecasts uses a regression framework which measures the bias and variance of the forecast. We show that the associated test for bias is inappropriate before introducing a more suitable procedure which is based on the test for bias in a conditional mean forecast. Although volatility has been the most common measure of the variability in a financial time series, in many situations confidence interval forecasts are required. We consider the evaluation of interval forecasts and present a regression‐based procedure which uses quantile regression to assess quantile estimator bias and variance. We use exchange rate data to illustrate the proposal by evaluating seven quantile estimators, one of which is a new non‐parametric autoregressive conditional heteroscedasticity quantile estimator. The empirical analysis shows that the new evaluation procedure provides useful insight into the quality of quantile estimators. Copyright © 1999 John Wiley & Sons, Ltd.     

Forecasting Stock Market Volatility in Central and Eastern European Countries

In recent years, considerable attention has focused on modelling and forecasting stock market volatility. Stock market volatility matters because stock markets are an integral part of the financial architecture in market economies and play a key role in channelling funds from savers to investors. The focus of this paper is on forecasting stock market volatility in Central and East European (CEE) countries. The obvious question to pose, therefore, is how volatility can be forecast and whether one technique consistently outperforms other techniques. Over the years a variety of techniques have been developed, ranging from the relatively simple to the more complex conditional heteroscedastic models of the GARCH family. In this paper we test the predictive power of 12 models to forecast volatility in the CEE countries. Our results confirm that models which allow for asymmetric volatility consistently outperform all other models considered. Copyright © 2011 John Wiley & Sons, Ltd.     

The role of jumps in the agricultural futures market on forecasting stock market volatility: New evidence

In this study, we explore the effect of cojumps within the agricultural futures market, and cojumps between the agricultural futures market and the stock market, on stock volatility forecasting. Also, we take into account large and small components of cojumps. We have several noteworthy findings. First, large jumps may lead to more substantial fluctuations and are more powerful than small jumps. The effect of cojumps and their decompositions on future volatility are mixed. Second, a model including large and small cojumps between the agricultural futures market and the stock market can achieve a higher forecasting accuracy, implying that large and small cojumps contain more useful predictive information than cojumps themselves. Third, our conclusions are robust based on various robustness tests such as the realized kernel, expanding forecasts, different forecasting windows, different jump tests, and different threshold values.     

Power transformation models and volatility forecasting

This paper considers the forecast accuracy of a wide range of volatility models, with particular emphasis on the use of power transformations. Where one‐period‐ahead forecasts are considered, the power autoregressive models are ranked first by a range of error metrics. Over longer forecast horizons, however, generalized autoregressive conditional heteroscedasticity models are preferred. A value‐at‐risk‐based forecast assessment indicates that, while the forecast errors are independent, they are not independent and identically distributed, although this latter result is sensitive to the choice of forecast horizon. Our results are robust across a number of different asset markets. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting volatility of emerging stock markets: linear versus non‐linear GARCH models

ARCH and GARCH models are substantially used for modelling volatility of time series data. It is proven by many studies that if variables are significantly skewed, linear versions of these models are not sufficient for both explaining the past volatility and forecasting the future volatility. In this paper, we compare the linear(GARCH(1,1)) and non‐linear(EGARCH) versions of GARCH model by using the monthly stock market returns of seven emerging countries from February 1988 to December 1996. We find that for emerging stock markets GARCH(1,1) model performs better than EGARCH model, even if stock market return series display skewed distributions. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal sampling frequency for volatility forecast models for the Indian stock markets

This paper evaluates the performance of conditional variance models using high‐frequency data of the National Stock Index (S&P CNX NIFTY) and attempts to determine the optimal sampling frequency for the best daily volatility forecast. A linear combination of the realized volatilities calculated at two different frequencies is used as benchmark to evaluate the volatility forecasting ability of the conditional variance models (GARCH (1, 1)) at different sampling frequencies. From the analysis, it is found that sampling at 30 minutes gives the best forecast for daily volatility. The forecasting ability of these models is deteriorated, however, by the non‐normal property of mean adjusted returns, which is an assumption in conditional variance models. Nevertheless, the optimum frequency remained the same even in the case of different models (EGARCH and PARCH) and different error distribution (generalized error distribution, GED) where the error is reduced to a certain extent by incorporating the asymmetric effect on volatility. Our analysis also suggests that GARCH models with GED innovations or EGRACH and PARCH models would give better estimates of volatility with lower forecast error estimates. Copyright © 2008 John Wiley & Sons, Ltd.